Bootstrap methods have been used by actuaries for a long time to predict future claims cash flows and their variability. This work aims to illustrate the use of bootstrap methods in practice, taking as an example the claims development data of the personal accident portfolio from the largest insurance company in Albania, over a period of 10 years. It is not the objective of this work to provide a theoretical analysis of the bootstrap methods, rather, this work focuses on highlighting the benefits of using bootstrap methods to predict the distribution of future claims development, and estimate the standard error, for a better risk assessment of liabilities within insurance companies. This work is divided into two well-differentiated phases: the first is to select the theoretical probability distribution that best fits the available claims dataset. Comparison of distributions is facilitated by the possibilities offered by the R programming languages. Both, the maximum likelihood parameter estimation method and the chi-square goddess goodness of fit test, are used to specify the probability distribution that best fits the data, among a family of predefined distributions. The results show that the Gamma distribution better describes the claim development data. The next phase is to use bootstrap methods, based on the selected distribution, to estimate the ultimate value of claims, the claims reserve, and their standard error.

Some studies related to the topological structure of semigroups are provided. In, [3], considering and investigating the properties of the collection A of all the proper uniformly strongly prime ideals of a Γ - semigroup S, such study starts by constructing a topology τA on A using a closure operator defined in terms of the intersection and inclusion relation among these ideals of Γ-semigroup S, which is a generalization of the semigroup. In this paper, we introduce three other classes of ideals in semigroups called maximal ideals, prime ideals and strongly irreducible ideals, respectively. Investigating properties of the collection M, B and S of all proper maximal ideals, prime ideals and strongly irreducible ideals, respectively, of a semigroup S, we construct the respective topologies on them. The respective obtained topological spaces are called the structure spaces of the semigroup S. We study several principal topological axioms and properties in those structure spaces of semigroup such as separation axioms, compactness and connectedness, etc.

Objective. The design and implementation of an online dashboard to support data-driven decision-making and joint coordination between health institutions and government bodies in the Balkan countries faced with new COVID-19 waves in the region. Methods. Shiny R dashboard tracks COVID-19 in real-time using a comparative approach to interactively visualize national-level data from various official sources. Results. The dashboard, named COVID-19 Situation in Balkan countries can be accessed online (COVID-19 Situation in Balkan countries). The daily situation in 11 Balkan countries focuses on similarities and differences between countries on a daily basis and since the beginning of the pandemic. The web resource features the most affected countries, the number of new cases, and fatality rates reported daily. Features also include rankings of the worst affected countries, information search and filtering, and a map component interactively showing daily information for each country comparatively. Conclusions. The dashboard for the COVID-19 situation in Balkan countries simplifies meaningful real-time information for public and health agencies regarding the COVID-19 situation in the whole Balkan region. The creation allows for a deep analysis of measures taken to face COVID-19 in a regional context, allowing for health policy updates and a better basis for collaboration among Balkan governments.

The CHA2DS2VASc score includes risk factors for coronary artery disease. The aim of this study is to show that the CHA2DS2VASc score calculated at the time of hospital admission may predict mortality and major adverse cardiovascular and cerebrovascular events (MACCE) in-hospital and at 30-day follow-up for patients with STEMI, who were subjected to primary percutaneous coronary intervention (p-PCI). A retrospective cohort study was performed at University Hospital Center ‘Mother Teresa’, in the Cardiology Department between June 2021 and September 2021. The CHA2DS2VASc score was calculated at the time of hospital admission for all of them. The study population was divided into 3 groups according to the CHA2DS2VASc score at the time of admission. A statistical control of result of hospital MACCE was done. As the result of multivariable analysis, smoking and CHA2DS2VASc groups were found to be independent MACCE predictors. The chances of developing MACCE were approximately 5 times higher in a patient of the third CHA2DS2VASc group, compared to that of the first group. CHA2DS2VASc groups are important to define the likelihood that MACCE will occur in patients with ascending STEMI who had undergone PCI. The ROC plot provided a visual representation of the accuracy of CHA2DS2VASc in predicting reinfarction and stroke. AUC 0.852 (95% C.I: 0.776-0.928) showed when CHA2DS2VASc has this predictive ability for morbidity and mortality. CHA2DS2VASc ≥ 4 can be used to determine risk of reinfarction and stroke.

Stochastic methods of reserves estimation serve to assess the technical provisions of outstanding claims and forecast cash payments of claims in the coming years. The chain ladder model developed by Mack is the more prevalent model. The main deficiency in the chain-ladder model is that the chain-ladder model depends on the last observation on the diagonal. If this last observation is an outlier, this outlier will be projected to the ultimate claim. One of the possibilities to smooth outliers on the last observed diagonal is to robustify such observations, making use of the maximum likelihood estimation along with the common Loss Development Factor (LDF) curve fitting and Cape Cod (CC) techniques. This paper aims to highlight the advantages of using these methods for the best estimate of claims reserves in the Domestic Motor Third Party Liability portfolio. The maximum–likelihood parameter estimation and Chi-square test, are used to specify the probability distribution that best fits the data. Using the Standard Chain Ladder method, LDF, and CC method the claims reserve is calculated based on the run-off triangles of paid claims or the run-off triangles of the incurred claims. Many times, the projections based on the paid claims are different than the projections based on the incurred claims. The solution for this problem is the Munich Chain Ladder method.